On the Lie structure of a prime associative superalgebra
Abstract
In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, $A$, over a ring of scalars $\Phi$ with $1/2\in \Phi$, if $L$ is a Lie ideal of $A$ and $W$ is a subalgebra of $A$ such that $[W, L]\subseteq W$, then either $L\subseteq Z$ or $W\subseteq Z$. Likewise, if $V$ is a submodule of $A$ and $[V, L]\subseteq V$, then either $V\subseteq Z$ or $L\subseteq Z$ or there exists an ideal of $A$, $M$, such that $0\not= [M,A]\subseteq V$. This work extends to prime superalgebras some results of I. N. Herstein, C. Lanski and S. Montgomery on prime algebras.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2013
- DOI:
- 10.48550/arXiv.1307.3243
- arXiv:
- arXiv:1307.3243
- Bibcode:
- 2013arXiv1307.3243L
- Keywords:
-
- Mathematics - Rings and Algebras;
- 16W55;
- 17A70;
- 17C70